AbstractWe present the fundamental stellar and planetary properties of the transiting planetary system WASP-13 within the framework of the Homogeneous Study of Transiting Systems (HoSTS). HoSTS aims to derive the fundamental stellar (Teff, [Fe/H], M★, R★) and planetary (Mpl, Rpl, Teq) physical properties of known transiting planets using a consistent methodology and homogeneous high-quality data set. Four spectral analysis techniques are independently applied to a Keck+HIRES spectrum of WASP-13 considering two distinct cases: unconstrained parameters and constrained log g from transit light curves. We check the derived stellar temperature against that from a different temperature diagnostic based on an INT+IDS Ha spectrum. The four unconstrained analyses render results that are in good agreement, and provide an improvement of 50% in the precision of Teff, and of 85% in [Fe/H] with respect to the WASP-13 discovery paper. The planetary parameters are then derived via the Monte Carlo Markov Chain modeling of the radial velocity and light curves, in iteration with stellar evolutionary models to derive realistic uncertainties. WASP-13 (1.187 ± 0.065 M☉; 1.574 ± 0.048 R☉) hosts a Saturn-mass, transiting planet (0.500 ± 0.037 MJup; 1.407 ± 0.052 RJup), and is at the end of its main-sequence lifetime (4-5.5 Gyr). Our analysis of WASP-13 showcases that both a detailed stellar characterization and transit modeling are necessary to well determine the fundamental properties of planetary systems, which are paramount in identifying and determining empirical relationships between transiting planets and their hosts.